Sunshine State Standards MA.7.G.2.1 Justify and apply formulas for surface area..of…pyramids…and cones. Also MA.7.G.2.2

Vocabulary regular pyramid slant height of a pyramid

Pyramid – A three dimensional figure in which one face, the base, is any polygon and the lateral faces are triangles that meet at a common vertex. vertex Pyramid

The length of the altitude is called the height. The altitude of a pyramid is the perpendicular segment from the vertex to the plane of the base. The length of the altitude is called the height. Height Pyramid

The base of a regular pyramid is a regular polygon, and the faces are congruent isosceles triangles. The diagram shows a square pyramid. The blue dashed line labeled l is the slant height of the pyramid, the distance from the vertex to the midpoint of an edge of the base.

Lateral Area and Surface Area of a Regular Pyramid Base Perimeter Slant Height B Surface Area Lateral Area Base Area

Additional Example 1A: Finding the Surface Area of a Pyramid Find the surface area of the pyramid. 1 2 S = B + Pl Use the formula. S = lw + Pl 1 2 B = lw S = (9 • 9) + (36)(10)‏ 1 2 Substitute. P = 4(9) = 36 S = 81 + 180 Add. S = 261 m2 The surface area is 261 square meters.

Additional Example 1B: Finding the Surface Area of a Pyramid Find the surface area of the pyramid. 1 2 S = B + Pl Use the formula. S = bh + Pl 1 2 B= ½bh. S = (12)(10.38) + (36)(6)‏ 1 2 S = 62.28 + 108 S = 170.28 The surface area is 170.28 m2.

Check It Out: Example 1A Find the surface area of each pyramid. S = B + Pℓ =(7)(7) + (28)(12) 1 2 S = 49 + 168 = 217 = 217 mm2

Check It Out: Example 1B Find the surface area of the pyramid 1 2 1 2 S = B + Pℓ B = (8)(6.9) = 27.6 S =27.6 + (8+8+8)(5.6) = 27.6 + 67.2 1 2 S = 94.8 = 94.8 m2